Educators Employ New Means

Educators Employ New Means To Draw Interest In Math

All of the glassy-eyed students who ever took calculus, who scribbled formulas as fast as their professors could scrawl them on blackboards, ought to meet Bob Decker.

Today, Professor Decker will be bouncing a rubber ball.

"Shall we take the data first?" asks the lanky, boyish-looking University of Hartford professor, armed with a stopwatch and a yardstick. Soon, students working in pairs tap computer keyboards, devising mathematical explanations for how high the ball rebounds, how many bounces it makes and how long it takes to stop bouncing.

Decker not only bounces balls, he drops balloons and swings pendulums to make sense of a subject many students have found abstract or irrelevant.

He is part of a new breed of instructors seeking to change the way calculus is taught. The changes, including increasing use of new classroom computers, are part of a larger movement shifting mathematics away from mind-numbing drills toward challenging, real-life problems.

Educators across the country have expressed alarm at America's poor performance in mathematics education, saying it could diminish the nation's supply of scientists and engineers and threaten its technological edge in the world.

Calculus is a branch of mathematics dealing with rates of change and growth. Created by Sir Isaac Newton and Baron Gottfried Wilhelm von Leibniz in the 1600s, it influenced progress in science, engineering and mathematics over the next three centuries. Today, it is used to solve problems such as designing the shape of an airplane wing, predicting the price of stocks or forecasting the spread of AIDS.

It is a building block for most branches of science and engineering and is used increasingly in areas such as business and economics, but students fail or drop out of calculus courses at rates approaching 50 percent.

"They don't see the connections or the reasons they are doing the course," said Ronald G. Douglas, vice provost for undergraduate studies at the State University of New York at Stony Brook.

Douglas organized two major national meetings in 1986 and 1987

that helped launch the calculus-reform movement.

The movement is fueled by new technology that has made the slide rule a relic. New computers and calculators not only solve complex equations instantly, they translate them visually into graphs, sometimes in eye-popping color.

"It changes the way you can teach math, the way you can teach calculus. And it also changes to an extent what you should teach," Douglas said.

The machines can spare students many hours of pencil-and-paper calculations.

"For the first time, we can focus on when and why you divide, on how algebra is essential for dealing with change, on the critical concepts of calculus as opposed to the mindless drill that has turned off millions and millions of people," said Steven Leinwand, a mathematics consultant with the state Department of Education.

The new machines "allow you to play with functions," he said. "Students can get their hands dirty and get a real understanding of why those concepts are important."

While scholars were rethinking how calculus is taught, the National Council of Teachers of Mathematics, in two widely publicized reports in 1989 and 1991, urged a major shift in the way all mathematics is taught.

The reports encouraged teachers to develop mathematical reasoning instead of the memorization of formulas, to link mathematics and its applications and to emphasize "conjecturing, inventing and problem-solving instead of mechanistic answer-finding."

The new approaches are showing up in places such as Decker's University of Hartford calculus class, where teams of students debate how best to deal with the data they obtained from the bouncing ball.

"Any way you want to do it," Decker tells one puzzled student. The young man and his partner begin tapping numbers into their computer.

At a nearby table, a young woman tries to figure out why the answer her computer flashes is not correct. "That's not close enough," she says. "That's really far off."

This is not the kind of mathematics many of these students remember from high school.

"In high school it was all on the blackboard," says Robert Schaller, a freshman from Easton, Pa. "You'd have to hand plot [the graphs], and it would take a long time. With computers and calculators it's 100 times faster."

His partner, John Rottkamp, a freshman from Long Island, says, "We did a falling balloon; we did interest rates. ... We've modeled the growth of a sunflower plant, experimented with the orbit of the Earth."

In traditional calculus classes, students "were being taught to manipulate things but not how to think about problems," said Decker's colleague John Williams, who, with Decker, has written a laboratory manual titled "Bringing Calculus to Life."

The labs have been used in classrooms from Harvard University to Hartford's Weaver High School.